The above string theoretical argument carries over to for example any 4d globally supersymmetric theory: If in a vacuum four supercharges are spontaneously broken, then there is a massless goldstino whose action is given by the VA action.If all other fields are massive, then this is actually the entire action of the theory at sufficiently low energies. If the pure VA model has an instability, then this would either render any partially SUSY breaking vacuum in any SUSY theory unstable, which seems absurd, or it does not necessarily imply a problem once other fields are included and therefore requires a model dependent study. Such a model dependent study for the KKLT model was not performed in [1]} for the anti-D3-brane uplift, so no conclusion regarding its stability can be reached based on the analysis in [1]}. In particular, for the anti-D3-brane in the KKLT scenario the SUSY breaking scale is set by the string scale at the bottom of the warped throat. This string scale is above the (warped down) KK scale so in addition to the light open and closed string states with masses below the warped down string scale, there are also many states from the KK tower that are lighter than the SUSY breaking scale. Furthermore, for a single anti-D3-brane at the bottom of a warped throat there is a massless U(1) gauge field [3]}, [4]} in addition to the massless goldstino. It is therefore impossible to remove all light fields from the theory by reducing the UV cutoff. Therefore, one cannot apply the results of [1]} to the anti-D3-brane uplift in KKLT.
